A181597 (N\{4})-perfect numbers, i.e., numbers m for which sigma(m)-4 = 2m, if 4|m, otherwise sigma(m) = 2m.

6, 12, 88, 1888, 32128, 521728, 1848964, 8378368, 34359083008, 549753192448

Offset: 1

Author

Vladimir Shevelev, Nov 01 2010, Nov 03 2010

Keywords

• nonn
• more

Comments

Or union of {6}, near-perfect numbers m (cf. A181595) for which d(m)=4, and all odd perfect numbers (if they exist). Note that (N\{2})-perfect numbers are numbers for which sigma(m)-2=2m, if m is even, and sigma(m)=2m, if m is odd. They are all even numbers of A045768 and all odd perfect numbers (if they exist).

Examples

			88 is in the sequence since sigma(88) = 180 and 180 - 4 = 2*88.
		

Crossrefs

Cf. A000396, A005101, A005820, A088832, A118372, A153501, A181595, A181596.

Extensions

Invalid term removed and a(8)-a(10) from Donovan Johnson, Sep 14 2013